I thought by signing up, you basically are “freezing” your Constitutional rights...
That is in a sense correct. If you are active duty, or called in as a Reservist, the UCMJ is the “law of the land”. The rights provided to you by the Constitution are secondary and would only apply to you in a civil sense.
US service members are subject to the uniform code of military justice, referred “ucmj”. The ucmj being independent of constitution.